It is a common misconception that Chinese characters are pictographs or ideograms. Actually Chinese characters can be classified into four types. Knowing these four types can help learners better understand the origin of characters and their meanings.

1. 象形 (xiàngxíng) pictograph

Yes, some characters really are pictographs. However, there forms have become altered or simplified over time so their meaning is not usually immediately obvious. A few common characters which are pictographs and there meanings in English are shown below.

日(sun), 山 (mountain), 羊 (sheep), 川 (river), 手 (hand), 木 (wood), 車 (vehicle)

Only about 4% of characters belong in this category.

2. 指事 (zhǐshì) pictograph for abstract words

The simplest example of characters used to define abstract words is 上 (up) and 下 (down). Another paired example is 本 (original) and 末 (final). This probably needs a little explanation. The two characters show a mark on a tree (木). When the mark is at the bottom this represents the original, when the mark is at the top of the tree it represents the final.

3. 會意 (huìyì) combination of radicals to give a new meaning

These characters combine two or more radicals to give a new meaning. An example is 明 (bright) formed by combining 日 (sun) and 月 (moon). I don't think the meaning of this one is particularly obvious. It could also logically refer to the Earth as it between the sun and the moon or refer to a planet or other object in space.

Another is example is 看 (to look) formed by the combination of 手 (hand) and 目 (eye).

4. 形聲 (xíngshēng) meaning radical plus phonetic component

The majority of Chinese characters fall into this category. These characters combine a phonetic element with a meaning element. A simple example is 馬 (mǎ; horse) a pictograph. The combination of 女 (woman) plus 馬 (mǎ) gives the character 媽 (mā; mother). One radical helps to indicate the meaning while the other indicates the pronunciation.

About 80% of Chinese characters fall into this category. The biggest problem with these type of characters is that changes in the pronunciation of characters over time mean the phonetic does not always indicate the exact pronunciation.

Note: The English terms for the categories used in Illustrated Account of Chinese Characters are (1) pictographs 象形 (2) indicatives 指事 (3) ideographs 會意 and (4)
phonetic compounds 形聲

References:

Chinese character - Wikipedia

Illustrated Account of Chinese Characters (漢字圖解)
(Chinese-English bilingual edition with Traditional Chinese characters)
Compiled by Guanghui Xie (謝光輝)
Joint Publishing, Hong Kong, 2003
ISBN: 9620420888

You can read a review of this book at David on Formosa.